Local SYZ metric identification conjecture for Ooguri–Vafa models

Let $\mathcal{M}^{0}$ be the local Ooguri–Vafa model, let $Q$ be the quotient group defining its SYZ mirror $\bar{\mathcal{M}}^{0}=\mathcal{M}^{0}/Q$, and fix sufficiently large $R$. Local metric identification conjecture. For some fixed large enough $R$, $\bar{\mathcal{M}}^{0}$ endowed with the hyperkähler quotient metric is isometric to $\mathcal{M}^{0}/Q$ endowed with the quotient metric of the Gaiotto–Moore–Neitzke hyperkähler metric. This is the local analogue of the earlier metric-identification conjecture and concerns the metrical aspect of SYZ mirror symmetry; the source gives no resolution.